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Exact Solutions to Task Allocation Problems

Author

Listed:
  • Andreas Ernst

    (CSIRO Mathematical and Information Sciences, Private Bag 10, Clayton South MDC, Clayton, VIC 3169, Australia)

  • Houyuan Jiang

    (Judge Business School, University of Cambridge, Trumpington Street, Cambridge CB2 1AG, United Kingdom)

  • Mohan Krishnamoorthy

    (CSIRO Mathematical and Information Sciences, Private Bag 10, Clayton South MDC, Clayton, VIC 3169, Australia)

Abstract

The task allocation problem (TAP) is one where a number of tasks or modules need to be assigned to a set of processors or machines at minimum overall cost. The overall cost includes the communication cost between tasks that are assigned to different processors and other costs such as the assignment cost and the fixed cost of using processors. Processors may have limited or unlimited capacities to perform tasks. Task allocation has been applied to the design of distributed computing systems and also in auto-manufacturing contexts. We present several integer programs and a column generation formulation for the uncapacitated and the capacitated TAP. Computational experiments are carried out to demonstrate computational capabilities of integer programming and the column generation formulations for the uncapacitated TAP (UTAP). Excellent results are obtained for the column generation formulation. We also report some computational experience for the capacitated TAP (CTAP).

Suggested Citation

  • Andreas Ernst & Houyuan Jiang & Mohan Krishnamoorthy, 2006. "Exact Solutions to Task Allocation Problems," Management Science, INFORMS, vol. 52(10), pages 1634-1646, October.
    • Handle: RePEc:inm:ormnsc:v:52:y:2006:i:10:p:1634-1646
    DOI: 10.1287/mnsc.1060.0578
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    References listed on IDEAS

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    1. Amitava Dutta & Gary Koehler & Andrew Whinston, 1982. "On Optimal Allocation in a Distributed Processing Environment," Management Science, INFORMS, vol. 28(8), pages 839-853, August.
    2. Cynthia Barnhart & Ellis L. Johnson & George L. Nemhauser & Martin W. P. Savelsbergh & Pamela H. Vance, 1998. "Branch-and-Price: Column Generation for Solving Huge Integer Programs," Operations Research, INFORMS, vol. 46(3), pages 316-329, June.
    3. Hamam, Yskandar & Hindi, Khalil S., 2000. "Assignment of program modules to processors: A simulated annealing approach," European Journal of Operational Research, Elsevier, vol. 122(2), pages 509-513, April.
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    Citations

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    Cited by:

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    2. A Lusa & C N Potts, 2008. "A variable neighbourhood search algorithm for the constrained task allocation problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(6), pages 812-822, June.
    3. Asef Nazari & Dhananjay Thiruvady & Aldeida Aleti & Irene Moser, 2016. "A mixed integer linear programming model for reliability optimisation in the component deployment problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(8), pages 1050-1060, August.
    4. Riezebos, Jan & Zhu, Stuart X., 2020. "Inventory control with seasonality of lead times," Omega, Elsevier, vol. 92(C).
    5. Han-Lin Li & Yao-Huei Huang & Shu-Cherng Fang, 2017. "Linear Reformulation of Polynomial Discrete Programming for Fast Computation," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 108-122, February.
    6. Giovanni Giallombardo & Houyuan Jiang & Giovanna Miglionico, 2016. "New Formulations for the Conflict Resolution Problem in the Scheduling of Television Commercials," Operations Research, INFORMS, vol. 64(4), pages 838-848, August.
    7. Han-Lin Li & Yao-Huei Huang & Shu-Cherng Fang, 2013. "A Logarithmic Method for Reducing Binary Variables and Inequality Constraints in Solving Task Assignment Problems," INFORMS Journal on Computing, INFORMS, vol. 25(4), pages 643-653, November.
    8. Gudmundsson, Jens & Hougaard, Jens Leth & Platz, Trine Tornøe, 2023. "Decentralized task coordination," European Journal of Operational Research, Elsevier, vol. 304(2), pages 851-864.
    9. Gülpınar, Nalan & Çanakoğlu, Ethem & Branke, Juergen, 2018. "Heuristics for the stochastic dynamic task-resource allocation problem with retry opportunities," European Journal of Operational Research, Elsevier, vol. 266(1), pages 291-303.
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